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Determining molecular weights of mixture components with the Martin balance
DETERMINING MOLECULAR WEIGHTS OF MIXTURE COMPONENTS WITH THE MARTIN BALANCE* I. A. R E V E L ' S K I I , R. I. BORODULINA a n d T. M. SOVAKOVA (Received 27 November 1963)
GAS chromatography has become a basic method for the quantitative and qualitative analysis of complex mixtures of organic compounds. However, in many cases, identification of certain components of the mixture represents a much more complex problem than the selection of separation conditions. Many authors have confirmed the possibility of identifying components by using the relation existing for homologous series between the logarithm of the retention volume (log V) and the number of carbon atoms in the molecule [1-4], but the qualitative analysis of unknow~ mixtures by retention volumes alone is not feasible. For the identification of unknown components of mixtures emerging from a chromatographic column, the Martin balance, a gas density detector can be of great assistance, signal depending on the density of the carrier gas and the gas sample flowing through it. The construction and properties of the detector are described in a paper by Martin [5] and in subsequent papers [6-7]. Only the layout of the detector and its operating principle are very briefly described below. The housing of the apparatus is made of copper ~ith several holes drilled in it; a layout is shown in Fig. 1. !
1'
9
3'
/:low fPorn
1
FIG. 1. Layout of the gas density detector (Martin balance). *Neftekhimiya 4, 1~o. 5, 804-810, 1964. 296
Molecular weights of mixture components
297
The flow from the chromatographic column enters the detector at point A, is separated into two approximately identical streams in channels 10 and 10', then passes through channels 8 and 8' and through channels 9 and 9', is recombined at the mutual outlet E. The pure carrier-gas enters the detector at point B, is separated into two approximately equal streams along channels 2 and 2', then passes through channels 3, 6, 7, and 3', 6', 7', recombining in chammls 9 and 9' with the gases from the chromatographic column and is discharged through the joint outlet E. The channels are constructed to form a bridge, the four arms of which are symmetrical and adjusted by rods 1 and 1'. When the pure carrier-gas flows through the measuring and reference lines, pressure in points 4 and 4' is equalized and equilibrium established in the system. If the carrier-gas emerging from the chromatographic column contains a volatile component, the gas densities in channel 10 and 10' change, equilibrium is disturbed in the system and through anemometer 5 which represents a sensitive thermocouple, gas flows through in proportion to density difference of gas entering from the column and of the pure carrier-gas. The anemometer signal which is proportional to the small density variations is then transmitted to the umplifier and the auto-recorder. Only pure carrier-gas flows through the anemometer therefore, the detector signal is independent of the thermal conductivity of the component to be detected but depends only on the density difference of the carrier-gas and the component and, as has been shown by Liberti [8] is due to the molecular weights of the gas and the carrier-gas investigated. The density of the pure carrier-gas dl, and of the gas at the outlet of the chromatographic column (when the component passes through the detector) dx, is given by the equation: dl_ M1" P RT ;
dz=
( n l M v - b n x • M x) P RT '
(1)
where n 1 and n x are the molar proportions and M 1 and M~ are the molecular weights of the carrier-gas and the unknow~ component. The difference between the two gas flow densities, recorded by the detector is:
n~(M~--M1) P "~d~-l=
RT
(2)
If a chromatogram is obtained of a mixture using another carrier-gas, with molecular weight Ms, an equation similar to (2) can be derived.
n~(i~--M~) P Ad~_~= RT
(3)
I.A. REVEL'SKIIet al.
298
The amount of substance x equal to Q, which has been chromatographed when using the first carrier-gas, can be expressed by the gas volume emerging from the chromatographic column GO
f n RT'x'P .dv
Qx= j
0
and substituting the value of n x from (2), we obtain: oO
Qx .Mx -
M1
f o
/tdx- 1" dv.
(4)
The standard amount of qk of substance k added to the mixture and chromatographed by the same method, is given by a similar expression:
qX=.MkM~kM1;Adk-l"dv,
(5)
0
where Adk-1 is the difference of two gas flow densities passing through the detector. Similar expressions are obtained for Q~ and q~ of compounds x and k when using the second carrier-gas with molecular weight M e. It has been experimentally shown that the electromotive force E of the anemometer thermocouple is proportional to the difference of gas flow densities for small density variations. This condition is observed using samples of several microlitres. The integrals are solved if we equate
0
Ad.dv=k f AE.dv.
(6)
0
Experimental values Qx and Q'x, qk and q~. cannot be directly measured with a high degree of accuracy but, since QJqz=Q'~/q'k,by the combination of the above equations and by the measurement of the respective areas of peaks Sx, S k, S~, S~, expressed in arbitrary units, we obtain an equation from which M~ can be calculated: Mk--M1
~
Mk--M 2
~ Mx--M1 S'~ Mx--M 2"
(7)
Irrespective of the fact that the properties of the Martin balance are wellknov~l, only two papers have been so far published on the use of the gas density detector for measuring molecular weights. The possibility of continuous determination of molecular weights of components to be eluted from the chromatographic column was theoretically shown
Molecular weights of mixture components
299
for any component and in practice b y the example of binary mixtures (one component is standard) in papers [8-9]. The error in determing molecular weights from these data was 4 ~ rel. Phillips and Timms [10] also used the density detector for the continuous measurement of molecular weights of components. However, the relative error of determination in their experiments was 5-10 ~ , therefore, they proposed to use the density detector to measure molecular weights of individual components in combination with the measurement of volume and vapour pressure of the sample. Only one paper [11] has been published on the use of the density detector to determine the quantitative composition of the mixtures without previous calibration of the detector. The purpose of our paper was to verify the possibility of using the density detector for the continuous determination of molecular weights of compo~mnts eluted from a chromatographic column and for the calculation of the quantitative composition of mixtures from the molecular weights of components without previous calibration of the detector according to each component. EXPERIMENTAL DETAILS AND RESULTS
The study was carried out in Griffin D-6 chromatographs with a gas density detector (modified Martin detector). A synthetic mixture, consisting of hexane, chloroform methyl cyelohexane, benzene and toluene, was seperated on a column with eellite 545 saturated with 1 0 ~ E301 type silicone oil. The length of the column is 2 m, internal diameter 4 ram, temperature of the thermostat 42 °. The velocity of nitrogen in the comparative and measuring lines was maintained at 40 ml/min, and the velocity of argon at 50 ml/min. The samples were introduced b y a device proposed and recommended b y Griffin for the instrument. The peak areas were calculated as the areas of triangles, from the product of the peak height by its width at half the height. The width of peaks was measured b y a MIR-12 comparator with an accuracy of up to 0.01 mm. The cltromatograms of the synthetic mixture are s h o ~ l in Fig. 2. The molecular weights of the mixture components were calculated from equation (7) which, as experiment showed, is valid under condition of strictly consta~t gas velocity during analysis and small density variations, i.e. on introduefilg samples of the order of 1-4 mierolitres. Methylcyclohexane was used as the standard. Data on the determination of molecular weights of synthetic mixture components are shown in Table 1. As can be seen ia Table 1, the mean relative error of determination (from three experiments) is less than 5 °ffo which does not exceed the error in cryoscopic determination of molecular weights of individual substances.
I. A. REVEL'SKII et al.
300
To estimate the possible relative error in the determination of molecular weights of components we express the value of M x from equation (7):
sx M 2 ( M ~ - - M , ) . S~k - - M I ( M k - - M 2 ) . ~ , "" k
M, =
s,
(s)
(Mk--M1) " Sk - - ( M k - - M2)" __ Sk Obviously, the error in calculating molecular weights depends basically on the accuracy of determination of ratios Sx/S k and S'=/S~. The error in calculating the ratios of peak areas of components to the standard area (Sx/S k and S'=/S'k) depends on the error in introducing the samples (reproducibility when introdacing the sample according to composition) and on the error in calculating the peak areas. The accuracy in determining peak areas depends on the constancy of carriergas velocity, uniformity and of extension of the chromatogram strip and on the error of calculating the peak area.
mV
b
x20 2
5
1
~Z
,,50
2 4
20.
rain
15
lO
5
FIG. 2. Chromatogram of a mixture of hexane (1), chlorofrom (2), benzene (3), methylcyclohexano (4) and toluene (5). Carrier-gas-nitrogen (a). Carrier-gas-argon (b).
Molecular weights of mixture components
301
In our experiments the variations of carrier-gas velocity did not exceed 0.5°/ rel., the variability of extension was 0 . 2 ~ rel., the error in calculating peak width (of the order of 3 ram) was 0 . 3 ~ tel. With always the same sample taken ill ~ proportion of 1 ~ rel., the reproducibility (when determining the ratio of peak areas of components to the standard error) can be 3 ~ rel. (as the relative error of the quotient). I n this case, it follows from formula (8) t h a t the relative error in the determination of molecular weights of components can be 6 ~ rel. To obtairl highly accurate determinations oi molecular weights, a concentration ratio must be ensured for the components standard studied for which the ratio of their peak areas approaches uni t y and the absolute value of the area is adequate. Formula (8) shows t h a t the relative error in the determination of molecular weights can further increase because in calculating the numerator and the fraction denominator, sufficiently close values have to be subtracted and the relative error of difference, as is well-know~, is higher in inverse ratio to the difference. Therefore, as follows from the same formula (8) with the increase of M2 a~.d with tl~e reduction of Mx the accuracy of determining Mx should increase. T A B L E 1. D E T E R M I N A T I O ~~ OF MOLECULAR W E I G H T S OF COMPONENTS IN A M I X T U R E
Component
Ratio of the peak i areas of the compo- i nent Sx and standard i Sk ~x
Hexane
Chloroform
:Benzene
Toluene
[N,]
Molecular weight
8'x/S~,[Ar] Calculated
0.574 O.574 0.582 0.753 0.772 0.747 0.574 0.586 0.574 1.23 1.21
0.568 0-561 0.554 0.804 0.785 0.778 O-529 0-520 0.527 1.18 1.20
1.23
1.20
Relative error, ~
Actual
89.9
86.2
4.3
116.3
119.4
2.6
76.8
78.1
1.7
90.7
92-1
1.6
Apparently, for the determination of molecular weights with carrier-gas, hydrogen and Freon-l,2 are more suitable, their respective molecular weights being 2 and 121. I t is also obvious t h a t with increased accuracy of introducing samples and standardizing experimental conditions, the error in the determination of molecular weights can be reduced.
302
I.A. REVEL'SKIIet al.
The molecular weight of an unknown substance can be determined using only one carrier-gas~ of the composition of the mixture is known. If C~ is the concentration of the compound to be analysed in the mixture Ck, the standard concentration, then
C., S;K
(9)
Ck Sk'Kk '
Mx Mk and K k - - are the correction coefficients consiwhere K x - - M~--M Mk--M dering the difference in the molecular weights of the component (Mx) and the carrier-gas (M). Transforming (9), we obtain
Mx= M"
C~" Sk" K k Sk. Kk--C k. sx "
(10)
I t follows from expression (10) that to increase the accurac:~ of determilfing molecular weight, it is necessary that with identical concentrations of the compound and standard studied, the molecular weight of the latter should be much higher than that of the compound analysed (Sk>>S,). Determining the quantitative composition of the mixture. The concentration of each component in the mixture was calculated as follows: On passing vapours having a component with mass q, and with molecular weight M x through the density detector, a signal proportional to the con: centration of the component and the difference of molecular weights of the component and the carrier-gas is transmitted:
qx=a'S"'x--MM ' where a is the constant of the device. It is obvious that the concentration of each component (~o by weight) is:
q, Cx--Vq x~
or C~=
M,--M
(11)
Mx--M Data for calculating the concentrations of compo~mnts in the mixture according to established molecular weights, without previous calibration of the detector, are given in Table 2. As can be seen in Table 2, the error in determining the concentrations of components in the mixture does not exceed 5~o rel., which is the same as the accuracy of quantitative analysis by a catharometer pre-heated according to each component.
Molecular w e i g h t s of m i x t u r e c o m p o n e n t s
303
TABLE 2. DETERMINATION OF THE QUANTITATIVE COMPOSITION* OF MIXTURE COMPONENTS FROM THE KNOWN I~IOLECULAR WEIGHTS OF COMPONENTS Carrier - g a s - n i t r o g e n i
C x , %
Relative error, ~,~
Component Calculated
Actual
t~q
Mixture Hexane Chloroform Benzene Methylcyclohexane Toluene
15,990 18,510 16,850 26,180 32,900
Hexane Chloroform Benzene Methylcyclohexane Toluene
6,248 6,710 6,916 10,430 12,610
] i : ! I
Mixture
No. 1 !l 110,400
, I iI~
14.47 16.76 15.26 23.71 29.80
14.60 17.39 14.82 23.63 29-56
14.56 15.64 16.13 24.24 29.37
14-83 16.02 15.48 24.29 29.38
0.9 3.6 3.0 0-3 0.8
No. 2
42,910
!
i I
1.8 2-4 4.2 O.2 0.04
* Average results of three experiments are shown in the Table. TABLE 3. D E T E R M I N A T I O N OF THE QUANTITATIVE COMPOSITION OF COMPONENTS OF UNKNOWN MIXTURES FROM THEIR MOLECULAR WEIGHTS (M~) CALCULATED FROM CHROMATOGRAPHIC RESULTS Carrier-gas-nitrogen Cx , %
Component Calculated ~q Hexane
Chloroform
Benzene
Methylcyclohexane
Toluene
16,150 15,460 15,540 19,160 18,800 18,080 17,500 17,120 16,660 27,000 25,860 25,670 33,500 33,500 31,720
113,300 108,700 107,700 113,300 108,700 107,700 t13,300 108,700 107,700 113,300 108,700 107,700 113,300 113,300 107,700
Actual
Relative error, 9o
i
14.26 14.23 14.43 16.91 17.29 16.79 15.45 15.74 15.47 23-83 23.78 23.84 29,56 28.97 29.46
14.60
17-39
14.82
23.63
29.56
2.3 2-5 1-2 2.8 0.6 3.5 4.3 6.2 4.4 0.9 0.6 0.9 2.0 0.3
304
I.A. REVEL'SKIIel al.
W h e n calculating the q u a n t i t a t i v e composition of a n u n k n o w n mixture, the p e r c e n t a g e of each c o m p o n e n t in the m i x t u r e can be d e t e r m i n e d from the molecular weights calculated from c h r o m a t o g r a p h i c tests. To verify the a c c u r a c y of the q u a n t i t a t i v e analysis of such mixtures, the c o n c e n t r a t i o n s of c o m p o n e n t s in a s y n t h e t i c m i x t u r e were calculated (mixture 1, Table 2) from the molecular weights (Table 1). The d a t a of e x p e r i m e n t s are g i v e n in Table 3. I t is a p p a r e n t from the d a t a of Table 3 t h a t the error in determining the c o n c e n t r a t i o n s of c o m p o n e n t s in u n k n o w n m i x t u r e from the molecular weights derived from the d a t a o b t a i n e d from the density detector, does n o t exceed 5 ~ rel.
SUMMARY 1. The molecular weights of c o m p o n e n t s in mixtures eluted from a chromat o g r a p h i c c o l u m n ~'ere determilled with a density detector (Martin balance); the error was less t h a n 5 ~ rel. 2. I t was f o u n d to be possible to determine concentrations of c o m p o n e n t s in the m i x t u r e s w i t h o u t previous calibration of the detector, with an error n o t exceeding 5 ~ rel. Translated by E. SE13{ERE REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
A. T. JAMES and A. J. P. MAItTIN, Biochem. J, 50, 679, 1952 J, @. tIAWKE, It. P. ttANSEN, F. B. SttOItLAND, J. Chromatogr. 2, 547, 1959 N. It. ItA¥, J. Appl. Chem. 4, 21, 1954 Ch. MEItitIT, Jr. and J. T. WALStt, Analyt. Chem. 34, No. 8, 903, 1962 A. J. P. MARTIN and A. T. JAMES, Biochem. J. 63, 138, 1956 C. W. MUNDA¥ and G. It. PItIMAVESI, Vapour Phase Chromatography, ed. by D. H. Desty, Butterworth Sci. Publ., London, 1957 E. A. JOHNSON, D. G. CItILDS and G. It. BEAVEN, J. Chromatogr. 4, 429, 1960 A. LIBERTI, L. CONTI and V. @RESCENZI, :Nature 178, No. 4541, 1067, 1956 A. LIBEItTI, L. CONTI and V. CItESCENZI, Atti. Accad. Nazl. Lincei, Rend., Classe Sei. Fis. Mat. e Nat. 20, 623, 1956 @. S. G. PHILLIPS and P. L. TIMMS, J. Chromatogr. 5, 131, 1961 C. E. It. JONES and D. KINSLEIt, 4th International Symposium on Gas Chromatography at VEB Leuna-Werke "Walter Ulbricht", 28th-31st May, 1963
GAS chromatography has become a basic method for the quantitative and qualitative analysis of complex mixtures of organic compounds. However, in many cases, identification of certain components of the mixture represents a much more complex problem than the selection of separation conditions. Many authors have confirmed the possibility of identifying components by using the relation existing for homologous series between the logarithm of the retention volume (log V) and the number of carbon atoms in the molecule [1-4], but the qualitative analysis of unknow~ mixtures by retention volumes alone is not feasible. For the identification of unknown components of mixtures emerging from a chromatographic column, the Martin balance, a gas density detector can be of great assistance, signal depending on the density of the carrier gas and the gas sample flowing through it. The construction and properties of the detector are described in a paper by Martin [5] and in subsequent papers [6-7]. Only the layout of the detector and its operating principle are very briefly described below. The housing of the apparatus is made of copper ~ith several holes drilled in it; a layout is shown in Fig. 1. !
1'
9
3'
/:low fPorn
1
FIG. 1. Layout of the gas density detector (Martin balance). *Neftekhimiya 4, 1~o. 5, 804-810, 1964. 296
Molecular weights of mixture components
297
The flow from the chromatographic column enters the detector at point A, is separated into two approximately identical streams in channels 10 and 10', then passes through channels 8 and 8' and through channels 9 and 9', is recombined at the mutual outlet E. The pure carrier-gas enters the detector at point B, is separated into two approximately equal streams along channels 2 and 2', then passes through channels 3, 6, 7, and 3', 6', 7', recombining in chammls 9 and 9' with the gases from the chromatographic column and is discharged through the joint outlet E. The channels are constructed to form a bridge, the four arms of which are symmetrical and adjusted by rods 1 and 1'. When the pure carrier-gas flows through the measuring and reference lines, pressure in points 4 and 4' is equalized and equilibrium established in the system. If the carrier-gas emerging from the chromatographic column contains a volatile component, the gas densities in channel 10 and 10' change, equilibrium is disturbed in the system and through anemometer 5 which represents a sensitive thermocouple, gas flows through in proportion to density difference of gas entering from the column and of the pure carrier-gas. The anemometer signal which is proportional to the small density variations is then transmitted to the umplifier and the auto-recorder. Only pure carrier-gas flows through the anemometer therefore, the detector signal is independent of the thermal conductivity of the component to be detected but depends only on the density difference of the carrier-gas and the component and, as has been shown by Liberti [8] is due to the molecular weights of the gas and the carrier-gas investigated. The density of the pure carrier-gas dl, and of the gas at the outlet of the chromatographic column (when the component passes through the detector) dx, is given by the equation: dl_ M1" P RT ;
dz=
( n l M v - b n x • M x) P RT '
(1)
where n 1 and n x are the molar proportions and M 1 and M~ are the molecular weights of the carrier-gas and the unknow~ component. The difference between the two gas flow densities, recorded by the detector is:
n~(M~--M1) P "~d~-l=
RT
(2)
If a chromatogram is obtained of a mixture using another carrier-gas, with molecular weight Ms, an equation similar to (2) can be derived.
n~(i~--M~) P Ad~_~= RT
(3)
I.A. REVEL'SKIIet al.
298
The amount of substance x equal to Q, which has been chromatographed when using the first carrier-gas, can be expressed by the gas volume emerging from the chromatographic column GO
f n RT'x'P .dv
Qx= j
0
and substituting the value of n x from (2), we obtain: oO
Qx .Mx -
M1
f o
/tdx- 1" dv.
(4)
The standard amount of qk of substance k added to the mixture and chromatographed by the same method, is given by a similar expression:
qX=.MkM~kM1;Adk-l"dv,
(5)
0
where Adk-1 is the difference of two gas flow densities passing through the detector. Similar expressions are obtained for Q~ and q~ of compounds x and k when using the second carrier-gas with molecular weight M e. It has been experimentally shown that the electromotive force E of the anemometer thermocouple is proportional to the difference of gas flow densities for small density variations. This condition is observed using samples of several microlitres. The integrals are solved if we equate
0
Ad.dv=k f AE.dv.
(6)
0
Experimental values Qx and Q'x, qk and q~. cannot be directly measured with a high degree of accuracy but, since QJqz=Q'~/q'k,by the combination of the above equations and by the measurement of the respective areas of peaks Sx, S k, S~, S~, expressed in arbitrary units, we obtain an equation from which M~ can be calculated: Mk--M1
~
Mk--M 2
~ Mx--M1 S'~ Mx--M 2"
(7)
Irrespective of the fact that the properties of the Martin balance are wellknov~l, only two papers have been so far published on the use of the gas density detector for measuring molecular weights. The possibility of continuous determination of molecular weights of components to be eluted from the chromatographic column was theoretically shown
Molecular weights of mixture components
299
for any component and in practice b y the example of binary mixtures (one component is standard) in papers [8-9]. The error in determing molecular weights from these data was 4 ~ rel. Phillips and Timms [10] also used the density detector for the continuous measurement of molecular weights of components. However, the relative error of determination in their experiments was 5-10 ~ , therefore, they proposed to use the density detector to measure molecular weights of individual components in combination with the measurement of volume and vapour pressure of the sample. Only one paper [11] has been published on the use of the density detector to determine the quantitative composition of the mixtures without previous calibration of the detector. The purpose of our paper was to verify the possibility of using the density detector for the continuous determination of molecular weights of compo~mnts eluted from a chromatographic column and for the calculation of the quantitative composition of mixtures from the molecular weights of components without previous calibration of the detector according to each component. EXPERIMENTAL DETAILS AND RESULTS
The study was carried out in Griffin D-6 chromatographs with a gas density detector (modified Martin detector). A synthetic mixture, consisting of hexane, chloroform methyl cyelohexane, benzene and toluene, was seperated on a column with eellite 545 saturated with 1 0 ~ E301 type silicone oil. The length of the column is 2 m, internal diameter 4 ram, temperature of the thermostat 42 °. The velocity of nitrogen in the comparative and measuring lines was maintained at 40 ml/min, and the velocity of argon at 50 ml/min. The samples were introduced b y a device proposed and recommended b y Griffin for the instrument. The peak areas were calculated as the areas of triangles, from the product of the peak height by its width at half the height. The width of peaks was measured b y a MIR-12 comparator with an accuracy of up to 0.01 mm. The cltromatograms of the synthetic mixture are s h o ~ l in Fig. 2. The molecular weights of the mixture components were calculated from equation (7) which, as experiment showed, is valid under condition of strictly consta~t gas velocity during analysis and small density variations, i.e. on introduefilg samples of the order of 1-4 mierolitres. Methylcyclohexane was used as the standard. Data on the determination of molecular weights of synthetic mixture components are shown in Table 1. As can be seen ia Table 1, the mean relative error of determination (from three experiments) is less than 5 °ffo which does not exceed the error in cryoscopic determination of molecular weights of individual substances.
I. A. REVEL'SKII et al.
300
To estimate the possible relative error in the determination of molecular weights of components we express the value of M x from equation (7):
sx M 2 ( M ~ - - M , ) . S~k - - M I ( M k - - M 2 ) . ~ , "" k
M, =
s,
(s)
(Mk--M1) " Sk - - ( M k - - M2)" __ Sk Obviously, the error in calculating molecular weights depends basically on the accuracy of determination of ratios Sx/S k and S'=/S~. The error in calculating the ratios of peak areas of components to the standard area (Sx/S k and S'=/S'k) depends on the error in introducing the samples (reproducibility when introdacing the sample according to composition) and on the error in calculating the peak areas. The accuracy in determining peak areas depends on the constancy of carriergas velocity, uniformity and of extension of the chromatogram strip and on the error of calculating the peak area.
mV
b
x20 2
5
1
~Z
,,50
2 4
20.
rain
15
lO
5
FIG. 2. Chromatogram of a mixture of hexane (1), chlorofrom (2), benzene (3), methylcyclohexano (4) and toluene (5). Carrier-gas-nitrogen (a). Carrier-gas-argon (b).
Molecular weights of mixture components
301
In our experiments the variations of carrier-gas velocity did not exceed 0.5°/ rel., the variability of extension was 0 . 2 ~ rel., the error in calculating peak width (of the order of 3 ram) was 0 . 3 ~ tel. With always the same sample taken ill ~ proportion of 1 ~ rel., the reproducibility (when determining the ratio of peak areas of components to the standard error) can be 3 ~ rel. (as the relative error of the quotient). I n this case, it follows from formula (8) t h a t the relative error in the determination of molecular weights of components can be 6 ~ rel. To obtairl highly accurate determinations oi molecular weights, a concentration ratio must be ensured for the components standard studied for which the ratio of their peak areas approaches uni t y and the absolute value of the area is adequate. Formula (8) shows t h a t the relative error in the determination of molecular weights can further increase because in calculating the numerator and the fraction denominator, sufficiently close values have to be subtracted and the relative error of difference, as is well-know~, is higher in inverse ratio to the difference. Therefore, as follows from the same formula (8) with the increase of M2 a~.d with tl~e reduction of Mx the accuracy of determining Mx should increase. T A B L E 1. D E T E R M I N A T I O ~~ OF MOLECULAR W E I G H T S OF COMPONENTS IN A M I X T U R E
Component
Ratio of the peak i areas of the compo- i nent Sx and standard i Sk ~x
Hexane
Chloroform
:Benzene
Toluene
[N,]
Molecular weight
8'x/S~,[Ar] Calculated
0.574 O.574 0.582 0.753 0.772 0.747 0.574 0.586 0.574 1.23 1.21
0.568 0-561 0.554 0.804 0.785 0.778 O-529 0-520 0.527 1.18 1.20
1.23
1.20
Relative error, ~
Actual
89.9
86.2
4.3
116.3
119.4
2.6
76.8
78.1
1.7
90.7
92-1
1.6
Apparently, for the determination of molecular weights with carrier-gas, hydrogen and Freon-l,2 are more suitable, their respective molecular weights being 2 and 121. I t is also obvious t h a t with increased accuracy of introducing samples and standardizing experimental conditions, the error in the determination of molecular weights can be reduced.
302
I.A. REVEL'SKIIet al.
The molecular weight of an unknown substance can be determined using only one carrier-gas~ of the composition of the mixture is known. If C~ is the concentration of the compound to be analysed in the mixture Ck, the standard concentration, then
C., S;K
(9)
Ck Sk'Kk '
Mx Mk and K k - - are the correction coefficients consiwhere K x - - M~--M Mk--M dering the difference in the molecular weights of the component (Mx) and the carrier-gas (M). Transforming (9), we obtain
Mx= M"
C~" Sk" K k Sk. Kk--C k. sx "
(10)
I t follows from expression (10) that to increase the accurac:~ of determilfing molecular weight, it is necessary that with identical concentrations of the compound and standard studied, the molecular weight of the latter should be much higher than that of the compound analysed (Sk>>S,). Determining the quantitative composition of the mixture. The concentration of each component in the mixture was calculated as follows: On passing vapours having a component with mass q, and with molecular weight M x through the density detector, a signal proportional to the con: centration of the component and the difference of molecular weights of the component and the carrier-gas is transmitted:
qx=a'S"'x--MM ' where a is the constant of the device. It is obvious that the concentration of each component (~o by weight) is:
q, Cx--Vq x~
or C~=
M,--M
(11)
Mx--M Data for calculating the concentrations of compo~mnts in the mixture according to established molecular weights, without previous calibration of the detector, are given in Table 2. As can be seen in Table 2, the error in determining the concentrations of components in the mixture does not exceed 5~o rel., which is the same as the accuracy of quantitative analysis by a catharometer pre-heated according to each component.
Molecular w e i g h t s of m i x t u r e c o m p o n e n t s
303
TABLE 2. DETERMINATION OF THE QUANTITATIVE COMPOSITION* OF MIXTURE COMPONENTS FROM THE KNOWN I~IOLECULAR WEIGHTS OF COMPONENTS Carrier - g a s - n i t r o g e n i
C x , %
Relative error, ~,~
Component Calculated
Actual
t~q
Mixture Hexane Chloroform Benzene Methylcyclohexane Toluene
15,990 18,510 16,850 26,180 32,900
Hexane Chloroform Benzene Methylcyclohexane Toluene
6,248 6,710 6,916 10,430 12,610
] i : ! I
Mixture
No. 1 !l 110,400
, I iI~
14.47 16.76 15.26 23.71 29.80
14.60 17.39 14.82 23.63 29-56
14.56 15.64 16.13 24.24 29.37
14-83 16.02 15.48 24.29 29.38
0.9 3.6 3.0 0-3 0.8
No. 2
42,910
!
i I
1.8 2-4 4.2 O.2 0.04
* Average results of three experiments are shown in the Table. TABLE 3. D E T E R M I N A T I O N OF THE QUANTITATIVE COMPOSITION OF COMPONENTS OF UNKNOWN MIXTURES FROM THEIR MOLECULAR WEIGHTS (M~) CALCULATED FROM CHROMATOGRAPHIC RESULTS Carrier-gas-nitrogen Cx , %
Component Calculated ~q Hexane
Chloroform
Benzene
Methylcyclohexane
Toluene
16,150 15,460 15,540 19,160 18,800 18,080 17,500 17,120 16,660 27,000 25,860 25,670 33,500 33,500 31,720
113,300 108,700 107,700 113,300 108,700 107,700 t13,300 108,700 107,700 113,300 108,700 107,700 113,300 113,300 107,700
Actual
Relative error, 9o
i
14.26 14.23 14.43 16.91 17.29 16.79 15.45 15.74 15.47 23-83 23.78 23.84 29,56 28.97 29.46
14.60
17-39
14.82
23.63
29.56
2.3 2-5 1-2 2.8 0.6 3.5 4.3 6.2 4.4 0.9 0.6 0.9 2.0 0.3
304
I.A. REVEL'SKIIel al.
W h e n calculating the q u a n t i t a t i v e composition of a n u n k n o w n mixture, the p e r c e n t a g e of each c o m p o n e n t in the m i x t u r e can be d e t e r m i n e d from the molecular weights calculated from c h r o m a t o g r a p h i c tests. To verify the a c c u r a c y of the q u a n t i t a t i v e analysis of such mixtures, the c o n c e n t r a t i o n s of c o m p o n e n t s in a s y n t h e t i c m i x t u r e were calculated (mixture 1, Table 2) from the molecular weights (Table 1). The d a t a of e x p e r i m e n t s are g i v e n in Table 3. I t is a p p a r e n t from the d a t a of Table 3 t h a t the error in determining the c o n c e n t r a t i o n s of c o m p o n e n t s in u n k n o w n m i x t u r e from the molecular weights derived from the d a t a o b t a i n e d from the density detector, does n o t exceed 5 ~ rel.
SUMMARY 1. The molecular weights of c o m p o n e n t s in mixtures eluted from a chromat o g r a p h i c c o l u m n ~'ere determilled with a density detector (Martin balance); the error was less t h a n 5 ~ rel. 2. I t was f o u n d to be possible to determine concentrations of c o m p o n e n t s in the m i x t u r e s w i t h o u t previous calibration of the detector, with an error n o t exceeding 5 ~ rel. Translated by E. SE13{ERE REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
A. T. JAMES and A. J. P. MAItTIN, Biochem. J, 50, 679, 1952 J, @. tIAWKE, It. P. ttANSEN, F. B. SttOItLAND, J. Chromatogr. 2, 547, 1959 N. It. ItA¥, J. Appl. Chem. 4, 21, 1954 Ch. MEItitIT, Jr. and J. T. WALStt, Analyt. Chem. 34, No. 8, 903, 1962 A. J. P. MARTIN and A. T. JAMES, Biochem. J. 63, 138, 1956 C. W. MUNDA¥ and G. It. PItIMAVESI, Vapour Phase Chromatography, ed. by D. H. Desty, Butterworth Sci. Publ., London, 1957 E. A. JOHNSON, D. G. CItILDS and G. It. BEAVEN, J. Chromatogr. 4, 429, 1960 A. LIBERTI, L. CONTI and V. @RESCENZI, :Nature 178, No. 4541, 1067, 1956 A. LIBEItTI, L. CONTI and V. CItESCENZI, Atti. Accad. Nazl. Lincei, Rend., Classe Sei. Fis. Mat. e Nat. 20, 623, 1956 @. S. G. PHILLIPS and P. L. TIMMS, J. Chromatogr. 5, 131, 1961 C. E. It. JONES and D. KINSLEIt, 4th International Symposium on Gas Chromatography at VEB Leuna-Werke "Walter Ulbricht", 28th-31st May, 1963